List of top Questions asked in Bihar Board Class X Exam

If \( a \cos \theta + b \sin \theta = 4 \) and \( a \sin \theta - b \cos \theta = 3 \), then the value of \( a^2 + b^2 \) is
The simplest form of \( 0.\overline{3} + 0.\overline{4} \) is
If \( 156 = 2^x \times 3^y \times 13^z \), then \( x + y + z = ? \)
\( \sqrt{10} \times \sqrt{15} \) is
In the form of \( \frac{p}{2^n \times 5^m} \), \( 0.105 \) can be written as
If H.C.F. of two numbers = 25 and L.C.M = 50, then the product of the numbers will be
If in division algorithm \( a = bq + r \), \( b = 61 \), \( q = 27 \), and \( r = 32 \), what is the value of \( a \)?
If \( q \) is a positive integer, which of the following is an odd positive integer?
If the ratio of corresponding sides of two similar triangles is 5:6, then the ratio of their perimeters is
In \( \triangle ABC \), \( AB = 6\sqrt{3} \, \text{cm}, AC = 12 \, \text{cm}, \) and \( BC = 6 \, \text{cm} \), then \( \angle B \) is
If one side of an equilateral triangle \( ABC \) is 12 cm and one side of equilateral triangle \( DEF \) is 6 cm, then the ratio of areas of \( \frac{\triangle ABC}{\triangle DEF} \) is:
If \( \triangle ABC \) and \( \triangle PQR \) are similar triangles in which \( AD \) is perpendicular from vertex \( A \) to \( BC \) and \( PT \) is perpendicular from vertex \( P \) to \( QR \), \( AD = 9 \, \text{cm} \) and \( PT = 7 \, \text{cm} \), then the ratio of areas of triangle \( \triangle AB \) and triangle \( \triangle PQR \) is
If one side of an equilateral triangle is 12 cm, then its height is
\( \sqrt{\frac{64}{81}} + \sqrt{\frac{16}{9}} \) is
The product of two irrational numbers \( 3 + \sqrt{6} \) and \( 3 - \sqrt{5} \) will be a/an
If the sum of the first \( n \) terms of an A.P. is \( (5n - n^2) \), then the common difference of the A.P. is
If \( P \left( \frac{a}{2}, 4 \right) \) is the midpoint of the line segment joining the points \( A (-6, 5) \) and \( B (-2, 3) \), then the value of \( a \) is
If three points are collinear, then what is the area of the triangle made by them?
If \( A(-1, 0), B(5, -2) \), and \( C(8, 2) \) are the vertices of a triangle, the coordinates of its centroid are
If in \( \triangle ABC \), \( AD \) is the bisector of \( \angle BAC \) and \( AB = \frac{1}{10} \, \text{cm}, AC = 14 \, \text{cm}, BC = 6 \, \text{cm} \), then the value of \( DC \) is
In \( \triangle ABC \), \( DE \parallel BC \) such that \( \frac{AD}{DB} = \frac{3}{5} \). If \( AC = 5.6 \, \text{cm} \), then \( AE \)= ?
The 2nd term of an A.P. is 13 and its 5th term is 25. The common difference of the A.P. is
The pair of linear equations \( 2x - 3y = 8 \) and \( 4x - 6y = 9 \) are
The graphs of the equations \( 2x + 3y = 4 \) and \( 4x + 6y = 12 \) are which type of straight lines?
How many solutions does the system of linear equations \( 2x - 3y + 1 = 0 \) and \( 3x + y + 2 = 0 \) have?